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Acta Cryst. (2009). E65, m410    [ doi:10.1107/S1600536809008824 ]

catena-Poly[[[diaquaterbium(III)]-[mu]-6-carboxynicotinato-[mu]-pyridine-2,5-dicarboxylato] dihydrate]

S. Li, F.-L. Zhang, S.-B. Wang and H.-L. Bai

Abstract top

The title compound, {[Tb(C7H3NO4)(C7H4NO4)(H2O)2]·2H2O}n, is isotypic with the analogous TmIII compound [Li, Zhang, Wang & Bai (2009). Acta Cryst. E65, m411]. The TbIII atom is octacoordinated by two water molecules and by four carboxylate O atoms and two pyridyl N atoms from two pyridine-2,5-dicarboxylate (2,5-pydc) and two 6-carboxynicotinate (2,5-Hpydc) ligands. The 2,5-pydc and 2,5-Hpydc ligands bridge TbIII atoms, generating helical coordination polymers along [001]. An extensive network of O-H...O hydrogen bonds is formed between the coordination polymers and the uncoordinated water molecules. The refined Flack parameter of 0.54 (2) suggests inversion twinning.

Comment top

The asymmetric unit of the title compound is shown in Fig. 1. Atom Tb1 displays octa-coordination through two water molecules, four carboxylate O atoms and two pyridyl N atoms from two 2,5-pydc and two 2,5-Hpydc ligands (2,5-pydc = pyridine-2,5-dicarboxylate). The 2,5-pydc and 2,5-Hpydc ligands bridge between TbIII atoms to generate helical coordination polymers along [001] (Fig. 2). An extensive network of O—H···O hydrogen bonds is formed between the coordination polymers and the lattice water molecules (Table 1 and Fig. 3).

Related literature top

For the isomorphous TmIII compound, see Li et al. (2009). For other related structures, see: Huang et al. (2007).

Experimental top

A mixture of terbium oxide (0.5 mmol), pyridine-2,5-dicarboxylic acid (0.5 mmol), in H2O (8 ml) and ethanol (8 ml) was sealed in a 25 ml Teflon-lined stainless steel autoclave and kept at 413 K for three days. Colourless crystals were obtained after cooling to room temperature with a yield of 27%. Elemental analysis calculated for C14H15N2TbO12: C 30.68, H 2.74, N 5.11%; Found: C 30.62, H 2.72, N 5.06%.

Refinement top

H atoms bound to C atoms were placed in calculated positions with C—H = 0.93 Å and refined as riding with Uiso(H) = 1.2Ueq(C). H atoms of the water molecules were placed so as to form a reasonable H-bond network and refined as riding with Uiso(H) = 1.5Ueq(O). The Flack parameter was refined as a full least-squares variable, and the refined value of 0.54 (2) suggests inversion twinning.

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT-Plus (Bruker, 2001); data reduction: SAINT-Plus (Bruker, 2001); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: SHELXTL (Sheldrick, 2008); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures top
[Figure 1] Fig. 1. Asymmetric unit of the title compound, showing 50% probability displacement ellipsoids for non-H atoms.
[Figure 2] Fig. 2. One-dimensional coordination polymer running along [001].
[Figure 3] Fig. 3. Projection along [001], showing the tetragonal arrangement of coordination polymers. O—H···O hydrogen bonds are shown as dashed lines.
catena-Poly[[[diaquaterbium(III)]-µ-6-carboxynicotinato-µ- pyridine-2,5-dicarboxylato] dihydrate] top
Crystal data top
[Tb(C7H3NO4)(C7H4NO4)(H2O)2]·2H2ODx = 2.202 Mg m−3
Mr = 562.20Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I4Cell parameters from 3001 reflections
Hall symbol: I -4θ = 1.9–25.3°
a = 15.107 (2) ŵ = 4.25 mm−1
c = 14.8587 (15) ÅT = 298 K
V = 3391.1 (7) Å3Block, colourless
Z = 80.12 × 0.11 × 0.08 mm
F(000) = 2192
Data collection top
Bruker APEXII CCD
diffractometer		3001 independent reflections
Radiation source: fine-focus sealed tube2886 reflections with I > 2σ(I)
graphiteRint = 0.072
φ and ω scansθmax = 25.3°, θmin = 1.9°
Absorption correction: multi-scan
(SADABS; Bruker, 2001)		h = −12→18
Tmin = 0.617, Tmax = 0.713k = −18→17
6901 measured reflectionsl = −13→17
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.053H-atom parameters constrained
wR(F2) = 0.131 w = 1/[σ2(Fo2) + (0.1007P)2 + 0.8682P]
where P = (Fo2 + 2Fc2)/3
S = 1.03(Δ/σ)max < 0.001
3001 reflectionsΔρmax = 3.51 e Å−3
263 parametersΔρmin = −1.17 e Å−3
0 restraintsAbsolute structure: Flack (1983), 1387 Freidel pairs
Primary atom site location: structure-invariant direct methodsFlack parameter: 0.54 (2)
Crystal data top
[Tb(C7H3NO4)(C7H4NO4)(H2O)2]·2H2OZ = 8
Mr = 562.20Mo Kα radiation
Tetragonal, I4µ = 4.25 mm−1
a = 15.107 (2) ÅT = 298 K
c = 14.8587 (15) Å0.12 × 0.11 × 0.08 mm
V = 3391.1 (7) Å3
Data collection top
Bruker APEXII CCD
diffractometer		3001 independent reflections
Absorption correction: multi-scan
(SADABS; Bruker, 2001)		2886 reflections with I > 2σ(I)
Tmin = 0.617, Tmax = 0.713Rint = 0.072
6901 measured reflectionsθmax = 25.3°
Refinement top
R[F2 > 2σ(F2)] = 0.053H-atom parameters constrained
wR(F2) = 0.131Δρmax = 3.51 e Å−3
S = 1.03Δρmin = −1.17 e Å−3
3001 reflectionsAbsolute structure: Flack (1983), 1387 Freidel pairs
263 parametersFlack parameter: 0.54 (2)
0 restraints
Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > 2sigma(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Tb10.30210 (3)0.22535 (3)0.22736 (3)0.01388 (17)
C10.1833 (6)0.4100 (6)0.1946 (6)0.0116 (19)
C20.1334 (7)0.4753 (6)0.1553 (6)0.0148 (19)
H2A0.11280.52220.19000.018*
C30.1132 (7)0.4720 (7)0.0639 (7)0.019 (2)
H3A0.07960.51660.03760.023*
C40.1433 (6)0.4021 (6)0.0129 (7)0.015 (2)
C50.1879 (7)0.3364 (7)0.0575 (8)0.021 (2)
H5A0.20460.28640.02510.025*
C60.2161 (6)0.4123 (6)0.2921 (6)0.015 (2)
C70.1302 (7)0.3959 (7)−0.0870 (7)0.017 (2)
C80.1196 (7)0.1238 (6)0.1716 (7)0.014 (2)
C90.0975 (6)0.1488 (6)0.2710 (7)0.0129 (18)
C100.0233 (6)0.1192 (7)0.3157 (7)0.017 (2)
H10A−0.01950.08650.28540.021*
C110.0131 (7)0.1383 (7)0.4052 (7)0.018 (2)
H11A−0.03510.11580.43660.022*
C120.0768 (6)0.1929 (6)0.4506 (6)0.0115 (18)
C130.1449 (7)0.2207 (7)0.3980 (7)0.019 (2)
H13A0.18650.25770.42490.023*
C140.0684 (7)0.2114 (7)0.5505 (7)0.018 (2)
N10.1583 (5)0.2001 (5)0.3112 (6)0.0142 (16)
N20.2094 (5)0.3400 (5)0.1465 (6)0.0142 (17)
O10.2739 (5)0.3551 (4)0.3099 (5)0.0178 (15)
H10.30580.36430.35610.027*
O20.1862 (6)0.4677 (6)0.3436 (5)0.035 (2)
O30.1625 (5)0.3283 (5)−0.1271 (5)0.0212 (16)
O40.0921 (6)0.4561 (5)−0.1264 (5)0.0262 (18)
O50.1946 (5)0.1457 (5)0.1459 (5)0.0208 (16)
O60.0625 (5)0.0865 (5)0.1277 (5)0.0240 (17)
O70.0056 (6)0.1862 (6)0.5922 (6)0.033 (2)
O80.1326 (5)0.2550 (5)0.5846 (5)0.0214 (16)
O90.3704 (5)0.0819 (5)0.1997 (5)0.0240 (17)
H910.38220.07000.25430.036*
H920.42220.08490.17780.036*
O100.4504 (5)0.2736 (5)0.2620 (5)0.0236 (16)
H1010.46410.28680.20820.035*
H1020.48750.23270.27290.035*
O110.2668 (7)0.0205 (6)0.0225 (6)0.045 (2)
H1110.24520.05780.05930.068*
H1120.28120.0241−0.03270.068*
O120.1257 (7)−0.0901 (6)0.0634 (7)0.046 (2)
H1210.0724−0.08900.08180.068*
H1220.1145−0.08210.00790.068*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Tb10.0145 (3)0.0144 (3)0.0128 (2)0.00004 (17)−0.00014 (19)0.00015 (19)
C10.013 (5)0.011 (4)0.011 (4)−0.002 (4)0.001 (4)0.006 (4)
C20.022 (5)0.008 (4)0.014 (4)0.002 (4)0.007 (4)−0.001 (4)
C30.015 (5)0.020 (5)0.023 (5)0.007 (4)−0.002 (4)−0.001 (4)
C40.017 (5)0.013 (5)0.016 (5)−0.003 (4)−0.011 (4)0.000 (4)
C50.021 (5)0.016 (5)0.026 (5)0.005 (4)−0.007 (4)−0.009 (4)
C60.016 (5)0.012 (4)0.017 (6)−0.001 (4)0.002 (4)−0.008 (4)
C70.012 (5)0.020 (5)0.019 (5)0.000 (4)0.004 (4)−0.007 (4)
C80.023 (5)0.006 (4)0.012 (4)0.004 (4)−0.003 (4)−0.006 (4)
C90.018 (4)0.013 (4)0.008 (4)−0.002 (4)−0.002 (4)0.006 (4)
C100.014 (5)0.018 (5)0.020 (5)−0.001 (4)−0.003 (4)−0.004 (4)
C110.015 (5)0.023 (5)0.018 (5)0.000 (4)−0.007 (4)0.007 (4)
C120.008 (4)0.015 (4)0.012 (4)0.004 (4)0.008 (4)0.000 (4)
C130.018 (5)0.022 (5)0.017 (5)0.001 (4)−0.002 (4)−0.006 (4)
C140.014 (5)0.025 (6)0.014 (5)0.001 (5)−0.003 (4)−0.004 (4)
N10.013 (4)0.012 (4)0.018 (4)−0.001 (3)−0.001 (4)−0.002 (4)
N20.013 (4)0.015 (4)0.015 (4)0.003 (3)−0.002 (3)−0.002 (3)
O10.021 (3)0.016 (3)0.016 (3)−0.001 (3)−0.007 (3)−0.003 (3)
O20.050 (5)0.035 (5)0.019 (4)0.019 (4)−0.006 (4)−0.002 (4)
O30.020 (4)0.026 (4)0.017 (4)0.007 (3)−0.002 (3)−0.004 (3)
O40.032 (4)0.024 (4)0.022 (4)0.017 (3)−0.006 (3)−0.002 (3)
O50.017 (4)0.021 (4)0.024 (4)−0.003 (3)0.003 (3)−0.004 (3)
O60.019 (4)0.029 (4)0.024 (4)−0.005 (3)0.001 (3)−0.006 (3)
O70.030 (4)0.045 (5)0.024 (4)−0.016 (4)0.011 (4)−0.004 (4)
O80.019 (4)0.032 (4)0.013 (3)−0.010 (3)0.002 (3)−0.007 (3)
O90.025 (4)0.031 (4)0.016 (3)0.000 (3)0.008 (3)0.007 (3)
O100.021 (4)0.035 (4)0.014 (4)−0.001 (3)0.005 (3)0.006 (3)
O110.064 (6)0.039 (5)0.033 (5)0.012 (5)0.014 (5)−0.010 (4)
O120.053 (6)0.045 (6)0.039 (5)0.018 (5)−0.004 (5)0.011 (5)
Geometric parameters (Å, °) top
Tb1—O12.351 (7)C8—C91.560 (14)
Tb1—O52.356 (7)C9—N11.341 (12)
Tb1—O8i2.358 (7)C9—C101.379 (14)
Tb1—O3ii2.371 (7)C10—C111.368 (16)
Tb1—O102.412 (7)C10—H10A0.930
Tb1—O92.435 (8)C11—C121.435 (14)
Tb1—N22.531 (8)C11—H11A0.930
Tb1—N12.534 (8)C12—C131.359 (14)
C1—N21.335 (13)C12—C141.516 (13)
C1—C21.373 (13)C13—N11.343 (15)
C1—C61.531 (13)C13—H13A0.930
C2—C31.393 (15)C14—O71.195 (14)
C2—H2A0.930C14—O81.277 (12)
C3—C41.378 (15)O1—H10.850
C3—H3A0.930O3—Tb1i2.371 (7)
C4—C51.370 (15)O8—Tb1ii2.358 (7)
C4—C71.500 (15)O9—H910.850
C5—N21.363 (15)O9—H920.850
C5—H5A0.930O10—H1010.850
C6—O21.221 (13)O10—H1020.850
C6—O11.256 (12)O11—H1110.850
C7—O41.226 (13)O11—H1120.850
C7—O31.279 (13)O12—H1210.850
C8—O61.219 (12)O12—H1220.850
C8—O51.242 (13)
O1—Tb1—O5124.7 (3)O1—C6—C1114.1 (8)
O1—Tb1—O8i116.1 (3)O4—C7—O3123.3 (10)
O5—Tb1—O8i83.7 (2)O4—C7—C4119.3 (9)
O1—Tb1—O3ii81.4 (3)O3—C7—C4117.4 (9)
O5—Tb1—O3ii116.7 (3)O6—C8—O5127.2 (10)
O8i—Tb1—O3ii140.3 (2)O6—C8—C9117.9 (9)
O1—Tb1—O1078.8 (2)O5—C8—C9114.9 (8)
O5—Tb1—O10154.8 (3)N1—C9—C10121.9 (10)
O8i—Tb1—O1076.4 (2)N1—C9—C8114.6 (9)
O3ii—Tb1—O1072.5 (2)C10—C9—C8123.5 (9)
O1—Tb1—O9155.1 (2)C11—C10—C9119.4 (10)
O5—Tb1—O975.6 (3)C11—C10—H10A120.3
O8i—Tb1—O977.5 (3)C9—C10—H10A120.3
O3ii—Tb1—O975.8 (2)C10—C11—C12120.2 (10)
O10—Tb1—O984.9 (3)C10—C11—H11A119.9
O1—Tb1—N264.9 (3)C12—C11—H11A119.9
O5—Tb1—N274.0 (3)C13—C12—C11114.5 (9)
O8i—Tb1—N273.6 (3)C13—C12—C14124.7 (10)
O3ii—Tb1—N2142.3 (3)C11—C12—C14120.7 (9)
O10—Tb1—N2114.1 (3)N1—C13—C12126.4 (10)
O9—Tb1—N2139.8 (3)N1—C13—H13A116.8
O1—Tb1—N173.4 (3)C12—C13—H13A116.8
O5—Tb1—N165.5 (3)O7—C14—O8124.1 (10)
O8i—Tb1—N1145.1 (3)O7—C14—C12121.0 (10)
O3ii—Tb1—N172.1 (3)O8—C14—C12114.8 (9)
O10—Tb1—N1137.5 (3)C9—N1—C13117.4 (9)
O9—Tb1—N1108.2 (3)C9—N1—Tb1117.1 (7)
N2—Tb1—N182.1 (3)C13—N1—Tb1124.5 (7)
N2—C1—C2120.3 (9)C1—N2—C5118.7 (9)
N2—C1—C6115.4 (8)C1—N2—Tb1116.8 (6)
C2—C1—C6124.3 (9)C5—N2—Tb1124.4 (7)
C1—C2—C3120.6 (9)C6—O1—Tb1126.1 (6)
C1—C2—H2A119.7C6—O1—H1116.9
C3—C2—H2A119.7Tb1—O1—H1117.0
C4—C3—C2119.5 (9)C7—O3—Tb1i141.6 (7)
C4—C3—H3A120.2C8—O5—Tb1127.4 (6)
C2—C3—H3A120.2C14—O8—Tb1ii137.7 (6)
C5—C4—C3116.8 (9)Tb1—O9—H9196.6
C5—C4—C7119.9 (9)Tb1—O9—H92114.0
C3—C4—C7123.3 (9)H91—O9—H92100.6
N2—C5—C4123.9 (9)Tb1—O10—H10195.5
N2—C5—H5A118.0Tb1—O10—H102115.7
C4—C5—H5A118.0H101—O10—H102100.9
O2—C6—O1126.6 (9)H111—O11—H112132.5
O2—C6—C1119.3 (9)H121—O12—H12296.9
N2—C1—C2—C3−3.4 (15)O3ii—Tb1—N1—C1341.3 (8)
C6—C1—C2—C3174.1 (9)O10—Tb1—N1—C136.3 (10)
C1—C2—C3—C40.4 (15)O9—Tb1—N1—C13109.1 (8)
C2—C3—C4—C53.7 (15)N2—Tb1—N1—C13−111.0 (8)
C2—C3—C4—C7−175.7 (10)C2—C1—N2—C52.2 (14)
C3—C4—C5—N2−5.2 (16)C6—C1—N2—C5−175.6 (9)
C7—C4—C5—N2174.2 (10)C2—C1—N2—Tb1179.6 (7)
N2—C1—C6—O2−170.7 (9)C6—C1—N2—Tb11.9 (10)
C2—C1—C6—O211.7 (15)C4—C5—N2—C12.3 (16)
N2—C1—C6—O110.2 (12)C4—C5—N2—Tb1−174.9 (8)
C2—C1—C6—O1−167.4 (9)O1—Tb1—N2—C1−7.5 (6)
C5—C4—C7—O4−178.2 (10)O5—Tb1—N2—C1134.4 (7)
C3—C4—C7—O41.1 (16)O8i—Tb1—N2—C1−137.6 (7)
C5—C4—C7—O3−0.4 (15)O3ii—Tb1—N2—C121.2 (9)
C3—C4—C7—O3178.9 (9)O10—Tb1—N2—C1−71.1 (7)
O6—C8—C9—N1−171.3 (9)O9—Tb1—N2—C1176.6 (6)
O5—C8—C9—N17.9 (12)N1—Tb1—N2—C167.8 (7)
O6—C8—C9—C1010.5 (13)O1—Tb1—N2—C5169.7 (9)
O5—C8—C9—C10−170.3 (9)O5—Tb1—N2—C5−48.3 (8)
N1—C9—C10—C11−3.6 (15)O8i—Tb1—N2—C539.7 (8)
C8—C9—C10—C11174.4 (9)O3ii—Tb1—N2—C5−161.5 (7)
C9—C10—C11—C123.5 (15)O10—Tb1—N2—C5106.2 (8)
C10—C11—C12—C13−0.9 (14)O9—Tb1—N2—C5−6.1 (10)
C10—C11—C12—C14−177.4 (9)N1—Tb1—N2—C5−115.0 (8)
C11—C12—C13—N1−1.9 (15)O2—C6—O1—Tb1161.3 (8)
C14—C12—C13—N1174.5 (10)C1—C6—O1—Tb1−19.6 (12)
C13—C12—C14—O7178.6 (11)O5—Tb1—O1—C6−30.8 (9)
C11—C12—C14—O7−5.3 (15)O8i—Tb1—O1—C670.2 (8)
C13—C12—C14—O8−1.4 (14)O3ii—Tb1—O1—C6−147.4 (8)
C11—C12—C14—O8174.7 (9)O10—Tb1—O1—C6138.9 (8)
C10—C9—N1—C131.0 (14)O9—Tb1—O1—C6−171.0 (7)
C8—C9—N1—C13−177.2 (8)N2—Tb1—O1—C615.4 (8)
C10—C9—N1—Tb1169.6 (7)N1—Tb1—O1—C6−73.5 (8)
C8—C9—N1—Tb1−8.6 (10)O4—C7—O3—Tb1i12.3 (17)
C12—C13—N1—C91.8 (16)C4—C7—O3—Tb1i−165.4 (7)
C12—C13—N1—Tb1−165.8 (8)O6—C8—O5—Tb1176.0 (8)
O1—Tb1—N1—C9147.5 (7)C9—C8—O5—Tb1−3.1 (12)
O5—Tb1—N1—C95.4 (6)O1—Tb1—O5—C8−46.5 (9)
O8i—Tb1—N1—C935.5 (9)O8i—Tb1—O5—C8−164.1 (8)
O3ii—Tb1—N1—C9−126.4 (7)O3ii—Tb1—O5—C851.8 (8)
O10—Tb1—N1—C9−161.3 (6)O10—Tb1—O5—C8157.8 (7)
O9—Tb1—N1—C9−58.6 (7)O9—Tb1—O5—C8117.3 (8)
N2—Tb1—N1—C981.4 (7)N2—Tb1—O5—C8−89.3 (8)
O1—Tb1—N1—C13−44.8 (8)N1—Tb1—O5—C8−0.9 (8)
O5—Tb1—N1—C13173.0 (9)O7—C14—O8—Tb1ii23.9 (17)
O8i—Tb1—N1—C13−156.8 (7)C12—C14—O8—Tb1ii−156.1 (7)
Symmetry codes: (i) −x+1/2, −y+1/2, z−1/2; (ii) −x+1/2, −y+1/2, z+1/2.
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O1—H1···O12iii0.851.982.801 (12)162
O9—H91···O4ii0.851.862.706 (10)180
O9—H92···O4iv0.851.992.842 (11)180
O10—H101···O7i0.851.832.679 (11)179
O10—H102···O9iii0.852.153.000 (11)180
O11—H111···O50.852.002.851 (12)180
O11—H112···O2i0.851.912.758 (12)180
O12—H121···O6v0.852.153.000 (12)180
O12—H122···O6vi0.852.082.930 (13)180
Symmetry codes: (iii) y+1/2, −x+1/2, −z+1/2; (ii) −x+1/2, −y+1/2, z+1/2; (iv) −y+1, x, −z; (i) −x+1/2, −y+1/2, z−1/2; (v) −x, −y, z; (vi) y, −x, −z.
Table 1
Hydrogen-bond geometry (Å, °) top
D—H···AD—HH···AD···AD—H···A
O1—H1···O12i0.851.982.801 (12)162
O9—H91···O4ii0.851.862.706 (10)180
O9—H92···O4iii0.851.992.842 (11)180
O10—H101···O7iv0.851.832.679 (11)179
O10—H102···O9i0.852.153.000 (11)180
O11—H111···O50.852.002.851 (12)180
O11—H112···O2iv0.851.912.758 (12)180
O12—H121···O6v0.852.153.000 (12)180
O12—H122···O6vi0.852.082.930 (13)180
Symmetry codes: (i) y+1/2, −x+1/2, −z+1/2; (ii) −x+1/2, −y+1/2, z+1/2; (iii) −y+1, x, −z; (iv) −x+1/2, −y+1/2, z−1/2; (v) −x, −y, z; (vi) y, −x, −z.
Acknowledgements top

The authors are grateful for financial support from the Scientific Research Foundation of Outstanding Talented Persons of Henan Province (grant No. 74200510014).

references
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